物理信息神经网络在水文地质与工程地质中的应用研究综述

朱琳; 钱陈之皓; 宫辉力; 郭涛; 李帅; 叶淼

doi:10.13928/j.cnki.wrahe.2025.07.002

水利水电技术（中英文） ›› 2025, Vol. 56 ›› Issue (7) : 13 -25. DOI: 10.13928/j.cnki.wrahe.2025.07.002

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物理信息神经网络在水文地质与工程地质中的应用研究综述

朱琳 ¹^,²^,³^,⁴^,⁵ ,
钱陈之皓 ¹^,²^,³ ,
宫辉力 ¹^,²^,³^,⁴^,⁵ ,
郭涛 ⁶ ,
李帅 ¹^,²^,³ ,
叶淼 ¹^,²^,³

作者信息 +

Review of applications of Physics-Informed Neural Networks in hydrogeology and engineering geology

Lin ZHU ¹^,²^,³^,⁴^,⁵ ,
Chenzhihao QIAN ¹^,²^,³ ,
Huili GONG ¹^,²^,³^,⁴^,⁵ ,
Tao GUO ⁶ ,
Shuai LI ¹^,²^,³ ,
Miao YE ¹^,²^,³

Author information +

文章历史 +

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摘要

【目的】在水文地质与工程地质研究中，传统机理数值模型在模拟复杂物理过程时存在建模精度低、不确定性等问题，机器学习模型则存在数据需求量大和可解释性差的不足。物理信息神经网络(Physics-Informed Neural Networks, PINNs)作为一种结合物理定律和机器学习的新方法，能够为解决上述问题提供可行的方案。【方法】首先，通过整理近四年文献，系统梳理机理数值模型、机器学习模型以及机理-学习耦合模型在水文地质与工程地质领域的研究现状；其次，深入分析PINNs在该领域的最新应用；最后，阐述了PINNs在水文地质与工程地质领域发展中存在的问题，并对其今后的发展给出相关建议。【结果】研究发现，在水文地质与工程地质领域，PINNs部分解决了数值模型和机器学习模型中存在的数据稀缺、可解释性差和泛化性不足的问题，拥有广阔的应用前景。今后需要进一步解决其在鲁棒性、自适应权重分配和初边界条件处理方面的问题，深入挖掘其潜力。【结论】在未来研究中，建议耦合生成式模型或强化学习等模型，减少因数据质量和噪声对模型的影响，提高PINNs的鲁棒性；使用自适应学习算法和动态权重平衡机制，平衡损失函数各项权重，使PINNs模型输出矩阵满足正交条件，提高PINNs模型的计算效率；综合实际情况，选择优化激活函数、约束方式等，使PINNs模型收敛速度更快，结果更为精准。

Abstract

[Objective] In the research on hydrogeology and engineering geology, traditional mechanism-based numerical models often exhibit issues such as low modeling accuracy and high uncertainty when simulating complex physical processes, while machine learning models are limited by their substantial data demands and poor interpretability. Physics-Informed Neural Networks(PINNs), as a new computational method that combines physical laws and machine learning, can provide a feasible solution to the above-mentioned problems. [Methods] Firstly, recent literature from the past four years is systematically reviewed to summarize the current research status of mechanism-based numerical models, machine learning models, and mechanism-learning coupled models in the fields of hydrogeology and engineering geology. Secondly, an in-depth analysis of PINNs' latest applications in these fields is conducted. Finally, the existing limitations of PINNs in the fields of hydrogeology and engineering geology are expounded, and recommendations for future development are proposed. [Results] It is found that PINNs have partially addressed issues in numerical models and machine learning models, such as data scarcity, poor interpretability, and insufficient generalizability, demonstrating broad application prospects in hydrogeology and engineering geology. Future efforts should focus on resolving existing problems in robustness, adaptive weight allocation, and initial and boundary condition processing to further tap into their potential. [Conclusion] In future research, the following recommendations for further development are proposed. Generative models or reinforcement learning should be coupled to reduce the impact of data quality and noise on the model, thereby enhancing robustness. Adaptive learning algorithms and dynamic weight balancing mechanisms should be employed to balance the weights of each term in the loss function and ensure the output matrix of the PINNs model satisfies orthogonal conditions, thereby improving computational efficiency. Considering the actual situation, methods such as the activation function and constraint methods should be optimized for selection to achieve faster convergence and higher accuracy in PINN modeling.